We develop a reciprocal-space model that describes the (hkl) dependence of the broadened Bragg peakwidths produced by x-ray diffraction from a dislocated epilayer. We compare the model to experiments and find that it accurately describes the peakwidths of 16 different Bragg reflections in the [010] zone of both GaN and AlN heterolayers. Using lattice-distortion parameters determined by fitting the model to selected reflections, we estimate threading-dislocation densities for seven different GaN and AlGaN samples and find improved agreement with transmission electron microscopy measurements.

Heteroepitaxial growth of AlxGa1−xN alloy films on GaN results in large tensile strain due to the lattice mismatch. During growth, this strain is partially relieved both by crack formation and by the coupled introduction of dense misfit dislocation arrays. Extensive transmission electron microscopy measurements show that the misfit dislocations enter the film by pyramidal glide of half loops on the 1∕3⟨11̱23⟩∕{112̱2} slip system, which is a well-known secondary slip system in hcp metals. Unlike the hcp case, however, where shuffle-type dislocations must be invoked for this slip plane, we show that glide-type dislocations are also possible. Comparisons of measured and theoretical critical thicknesses show that fully strained films can be grown into the metastable regime, which we attribute to limitations on defect nucleation. At advanced stages of relaxation, interfacial multiplication of dislocations dominates the strain relaxation process. This work demonstrates that misfit dislocations are important mechanisms for relaxation of strained III-nitride heterostructures that can contribute significantly to the overall defect density.

Transmission electron microscopy and x-ray diffraction were used to assess the microstructure and strain of AlxGa1−xN(x=0.61–0.64) layers grown on AlN. The compressively-strained AlGaN is partially relaxed by inclined threading dislocations, similar to observations on Si-doped AlGaN by P. Cantu, F. Wu, P. Waltereit, S. Keller, A. E. Romanov, U. K. Mishra, S. P. DenBaars, and J. S. Speck [Appl. Phys. Lett. 83, 674 (2003)]; however, in our material, the dislocations bend before the introduction of any Si. The bending may be initiated by the greater lattice mismatch or the lower dislocation density of our material, but the presence of Si is not necessarily required. The relaxation by inclined dislocations is quantitatively accounted for with the model of A. E. Romanov and J. S. Speck [Appl. Phys. Lett. 83, 2569 (2003)], and we demonstrate the predicted linear dependence of relaxation on layer thickness. Notably, such relaxation was not found in tensile strained AlGaN grown on GaN [J. A. Floro, D. M. Follstaedt, P. Provencio, S. J. Hearne, and S. R. Lee, J. Appl. Phys. 96, 7087 (2004)], even though the same mechanism appears applicable.